Find the equation of the axis of symmetry for the parabola y = x^2 + 1 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify coefficients: Identify the coefficients of the quadratic equation. The given parabola is y = x^2 + 1, which can be compared to the standard form y = ax^2 + bx + c. Here, a = 1, b = 0, and c = 1.Use axis of symmetry formula: Use the formula for the axis of symmetry. The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by the equation x = -b/(2a).Substitute values into formula: Substitute the values of a and b into the formula. Substitute a = 1 and b = 0 into the formula x = -b/(2a) to find the axis of symmetry. x = -0/(2 * 1) x = 0Write axis of symmetry equation: Write the equation of the axis of symmetry. The axis of symmetry is a vertical line passing through the x-coordinate found in Step 3. Therefore, the equation of the axis of symmetry is x = 0.

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Find the equation of the axis of symmetry for the parabola $y = x^2 + 1$ . $\newline$ Simplify any numbers and write them as proper fractions, improper fractions, or integers. $\newline$ $\_\_$

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Algebra 2

Characteristics of quadratic functions: equations

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Q. Find the equation of the axis of symmetry for the parabola

y = x^2 + 1

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\_\_

Identify coefficients: Identify the coefficients of the quadratic equation. $\newline$ The given parabola is $y = x^2 + 1$ , which can be compared to the standard form $y = ax^2 + bx + c$ . $\newline$ Here, $a = 1$ , $b = 0$ , and $c = 1$ .
Use axis of symmetry formula: Use the formula for the axis of symmetry. $\newline$ The axis of symmetry for a parabola in the form $y = ax^2 + bx + c$ is given by the equation $x = -\frac{b}{2a}$ .
Substitute values into formula: Substitute the values of $a$ and $b$ into the formula. $\newline$ Substitute $a = 1$ and $b = 0$ into the formula $x = -\frac{b}{2a}$ to find the axis of symmetry. $\newline$ $x = -\frac{0}{2 \times 1}$ $\newline$ $x = 0$
Write axis of symmetry equation: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line passing through the $x$ -coordinate found in Step $3$ . $\newline$ Therefore, the equation of the axis of symmetry is $x = 0$ .